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This blog post contains everything about Dollars Function, including FGH and numbers.

What to solve first?

In order of importance:

• numbers with the lowest & level (Ultimate Array Notation III)

• numbers with least & symbols (Ultimate Array Notation II)

• many &'s solve on lowest to highest & order (Ultimate Array Notation I)

• brackets with the lowest arrow level (Extended Array Notation)

• brackets with the least number of entries (Array Notation)

• brackets with the lowest level (Extended Bracket Notation)

• least nested bracket with the smallest brackets in it (Bracket Notation)

2 _ * r halt
2 1 * r 2
2 [ * r 2
2 ] * l 3
3 * * l 3
3 _ _ r 4
4 1 _ l 5
4 _ _ l 7
4 [ 0 r 7
4 0 0 r 4
5 _ 1 r 6
5 1 1 l 5
6 1 1 r 6
6 _ 1 r 4
7 ] 0 r 9
8 * _ r 8
8 _ * r halt
9 _ * l 10
9 * * * 2
10 * _ l 10
10 1 1 l halt


FGH Bracket Notation

Bracket Notation FGH Exact value
a$[0] $$f_1(a)$$ $$a2$$ a$[1] $$f_2(a)$$ $$2^aa$$
a$[2] $$f_3(a)$$ a$[3] $$f_4(a)$$
a$[[0]] $$f_{\omega}(a)$$ a$[0][[0]] = a$a[[0]] $$f_{\omega}(f_1(a))$$ a$[1][[0]] $$f_{\omega}(f_2(a))$$
a$[[0]][[0]] $$f_{\omega}(f_\omega(a))$$ a$[1[0]] $$f_{\omega+1}(a)$$
a$[[0][0]] $$f_{\omega*2}(a)$$ a$[[1]] $$f_{\omega^2}(a)$$
a$[[2]] $$f_{\omega^3}(a)$$ a$[[[0]]] $$f_{\omega^{\omega}}(a)$$
a$[[[[0]]]] $$f_{\omega^{\omega^{\omega}}}(a)$$ a$[[[...[[0]]...]] $$f_{\varepsilon_{0}}(a)$$

Numbers Bracket Notation

Deal Group: 1000$[a] a means prefix, for example Glorious Deal = 1000$[100]

FGH Extended Bracket Notation

Extended Bracket Notation FGH
$$[0]_2$$ $$\varepsilon_{0}$$
$$[[0]_2]$$ $$\varepsilon_{0}+1$$
$$[1[0]_2]$$ $$\varepsilon_{0}+2$$
$$[[0][0]_2]$$ $$\varepsilon_{0}+\omega$$
$$[[0]_2[0]_2]$$ $$\varepsilon_{0}*2$$
$$[[[0]_2]]$$ $$\omega^{\varepsilon_{0}+1}$$
$$[[[[0]_2]]]$$ $$\omega^{\omega^{\varepsilon_{0}+1}}$$
$$[1]_2$$ $$\varepsilon_{1}$$
$$[2]_2$$ $$\varepsilon_{2}$$
$$[[0]]_2$$ $$\varepsilon_{\omega}$$
$$[[0]_2]_2$$ $$\varepsilon_{\varepsilon_{0}}$$
$$[0]_3$$ $$\zeta_{0}$$
$$[[0]_3]$$ $$\zeta_{0}+1$$
$$[[[0]_3]]$$ $$\omega^{\zeta_{0}+1}$$
$$[[[[0]_3]]]$$ $$\omega^{\omega^{\zeta_{0}+1}}$$
$$[[0]_3]_2$$ $$\varepsilon_{\zeta_{0}+1}$$
$$[[[0]_3]_2]_2$$ $$\varepsilon_{\varepsilon_{\zeta_{0}+1}}$$
$$[1]_3$$ $$\zeta_{1}$$
$$[[0]_3]_3$$ $$\zeta_{\zeta_{0}}$$
$$[0]_4$$ $$\eta_{0}$$
$$[0]_{[0]}$$ $$\varphi(\omega,0)$$
$$[0]_{[0]_{[0]}}$$ $$\varphi(\varphi(\omega,0),0)$$
$$[0,1]$$

$$\varphi(1,0,0)$$

Numbers Extended Bracket Notation

Dollars Group: 1000$[1000]_a No groups: BigDollars: 1000$[1000]_[1000]

Cash Group: 1000$$$[0 \rightarrow_{\{0\}\text{&}_a[0]} 1]$$ Ultimate Array Notation IV and higher Treasure Function It marks the ultimate limit of my notation. Current Definition: treasure(0) = 1 treasure(a) = a$$$[0 \rightarrow_{\{0\}\text{|0|}_{\{0\}\text{|0|}_{\{0\}\text{|0|}_{...}1}1}1} 1]$$

with treasure(a-1) nests

Treasure Numbers

Bronze Treasure = treasure(2)

Silver Treasure = treasure(3)

Emerald Treasure = treasure(4)

Golden Treasure = treasure(5)

Diamond Treasure = treasure(1000)

Legend Treasure = treasure1000(1000)